Tuesday, 4 October 2011

On April 16 2010, the SEC filed fraud charges against Goldman Sachs, the “great vampire squid wrapped around the face of humanity”. The case in court is that the bank claimed the assets in the fund ABACUS 2007-AC1 were selected by an independent advisor, when in fact they were selected by John Paulson to enable his funds to short the assets, and in making the claim, the bank deceived investors. However the case is usually presented as the bank being taken to court for acting immorally structuring an asset designed to fail and selling this on to unsuspecting clients (for example The New York Times’ report and their prediction in December 2009 or in the UK Jeremy Warner of The Telegraph). The vampire squid was sucking the life out of innocent investors.

The SEC could not take Goldman Sachs to court for acting unethically, the courts are about legality not morality. However, it would come as a surprise to many that, according to Catholic doctrine at least, there was probably not much morally wrong with Goldman’s actions.

In the third quarter of the thirteenth century, Thomas Aquinas worked on his SummaTheologica, integrating Aristotelian philosophy with Catholic doctrine and established himself as a “Doctor of the Church”. In the “Second part of the Second part” of the Summa, Aquinas addressed the issue of individual morality, including the concept of justice. One question the theologian considered was “Whether it is lawful to sell something for more than it is worth?” and examined a case presented by Stoic philosophers

A grain merchant from Alexandria arrives at Rhodes, which is gripped by famine. The merchant knows that other merchants are following him with plentiful supplies of grain, though the town’s inhabitants do not know this. How should the merchant price the grain he has? ( De Officiis Book 1, XII)

The Roman jurist Cicero (Tully) was typical in arguing that the merchant should not take advantage of the misfortune of the starving and charge a lower price based on the knowledge of the coming relief.

Aquinas disagrees

in the case cited, the goods are expected to be of less value at a future time, on account of the arrival of other merchants, which was not foreseen by the buyers. Wherefore the seller, since he sells his goods at the price actually offered him, does not seem to act contrary to justice through not stating what is going to happen. If however he were to do so, or if he lowered his price, it would be exceedingly virtuous on his part: although he does not seem to be bound to do this as a debt of justice. (Summa II.II Q77(A3) Reply to Obj. 4)

This is an almost shocking conclusion from a saint. To Aquinas, the merchant, having arrived at Rhodes, may think there are more grain shipments on the way, but does not know. Aquinas argues that

because the just price of things is not fixed with mathematical precision, but depends on a kind of estimate, so that a slight addition or subtraction would not seem to destroy the equality of justice. (Summa II.II Q77(A1) Reply to Obj 1, para 2)

It is not unjust to charge the higher price, since whether of not this price is ‘just’, or not, is uncertain.

Aquinas’ concept of the “equality of justice” comes from Book 5 of Aristotle’s NicomacheanEthics which had been translated into Latin in 1250. In Ethics, Aristotle considered the morality of economic exchange and argues that market exchange is not performed in order to generate a profit, for gain, but to correct for inequalities and to establish a social equilibrium. Using the example of a builder and a shoemaker, Aristotle argues that

The builder, then, must get from the shoemaker the latter’s work, and must himself give him in return his own. (Ethics p 79)

For justice to exist in the exchange, there needed to be an equality between the shoes the shoemaker produced and the results of the builders’ work. For such an equality to exist, there needed to be a measure of the value of the goods produced by the builder and the shoemaker to enable a just exchange . This measure, the price, was provided by money.

all things that are exchanged must somehow be comparable. It is for this end that money has been introduced, and it becomes in a sense an intermediate; for it measures all things. (Ethics p 79)

The relationship at the heart of the exchange between the shoemaker and the builder that Aristotle went on to establish was explained mathematically, as a geometric relationship. This was significant since Aristotle never used mathematics in addressing questions in physics.

However Aquinas’ use of an analogy with mathematics was not simply following Aristotle, he was re-interpreting in the context of contemporary events. The twelfth century had seen a “renaissance” in western Europe, a population explosion that brought with it Gothic architecture and a commercial revolution.

In the aftermath of the collapse of the Roman Empire in the west, the concept ofturpe lucrum, or ‘shameful gain’ emerged and merchants were restricted in what prices they could charge. As Europe emerged out of the ‘castellan’ society, characterised by isolated local lords held together by feudal service relations, into one of integrated trade networks, turpe lucrumwas no longer a feasible basis on which to run the economy. It was in this environment that Leonardo of Pisa, Fibonacci, published the Liber Abaci.

One aspect of the complexity of the transactions was to disguise usurious contracts. There is a subtle difference between usury, which is associated with charging for the use of money, and interest which is a compensation for loss. For example a farmer could lend a cow for a year and expect to be re-paid with a cow and a calf, since in the normal course of events a cow would give birth to a calf over the year. Interest could be charged on ‘productive’ assets, with the consequence that all, legitimate, medieval securities would be ‘asset backed’. Gold, being inorganic, was not productive and so charging for its use was unjust.

However, this attitude to money stifled innovation and so more complex structures emerged to disguise the charging of interest on a money loan. For example, the ‘triple contract’ enabled an entrepreneur to raise money to invest in a trading venture. At the heart of the triple contract was a partnership between the entrepreneur and investors, this was the first contract. The second contract would be an insurance contract taken out by the entrepreneur to insure against the loss the investors’ capital. The third contract was another ‘insurance’ contract given to the investors by the entrepreneur, where by the investors surrendered their rights to a share of the profit in exchanged for a fixed payment from the entrepreneur, this payment was guaranteed by the second contract. Not quite a Credit Default Swap but definitely credit insurance.

Eventually, in 1236, the canon (church) jurist, Alanus Anglicus, determined that turpe lucrum did not exist if the future price of the good was uncertain in the mind of the merchant and this ruling was embedded in Catholic doctrine some ten years later. Aquinas, in the Summawas integrating the theories of the newly translated Aristotle with emerging Catholic doctrine and existing commercial practice to argue that a profit was ‘just’ so long as it was uncertain and might lead to a loss, it entailed a ‘risk’.

Islamic societies had equally stringent prohibitions on usury, and so this alone cannot explain why Fibonacci would have such an influence in Europe. The key difference between the environment for medieval European merchants and their colleagues in the Middle East, India or China was the range of currencies being used, a consequence of the castellan society of the ‘Dark Ages’. For example there were 28 different currencies in Italy at one time or another and as Groetzman has observed

Reading Liber Abacione has the sense that Italian merchants of the 13th century operated in a world of complete relativism. With no central government, no dominant currency, and even competing faiths and heresies, value is expressed quite abstractly only in a set of relative relations to other items. (NBER Working Paper No. 10352, 2004)

It was in this environment that ‘arbitrage’, the process by which one commodity ‘arbitrates’ between the value of two other commodities, just as money ‘mediates’ between the value of two commodities, emerges and is discussed in the Liber.

Aristotle’s use of mathematics in examining the nature of exchange was first noted by the medieval proto-scientist, and Aquinas’ teacher, Albert the Great. This observation was important philosophically since it separated the measure from the measured, money does not share the same ‘nature’ as shoes. This seems insignificant today, but at the time it was an important conceptual development that spawned a ‘mania’ for measuring and mathematics such as that undertaken by the ‘Merton Calculators’.

The historian Joel Kaye has argued that the line of thought initiated by Albert and Aquinas developed by Oresme and the Calculators, was based on

the transformation of the conceptual model of the natural world ,…, [which] was strongly influenced by the rapid monetisation of European society taking place [between 1260–1380] (Kaye, p 1)

The scholars took their approach to nature having observed the operation of the markets that had emerged in the century before and in response

[were] more intent on examining how the system of exchange actually functioned than how it ought to function. (Kaye, pp 219-220)

Kaye, and a fellow historian, Alfred Crosby, believe this paradigm shift played a pivotal role in the development of European science. The process of this conceptual change is clear. Innovations in finance led to the development of vernacular mathematics encapsulated in theLiber Abaci and disseminated through abbaco schools. University based scholars then began to try and make sense of what was actually happening and tried to identify the essence of the markets, with Aquinas concluding that a profit was ‘fair’ provided that it was uncertain and came with the risk of a loss. In modern terms, a market was viable if it did not admit arbitrages, so long as there is ‘No free lunch with vanishing risk’.

In much of the public discourse on modern finance, financial institutions are presented as immoral and rapacious beasts, initiating ‘unnatural’ financial instruments in order to take advantage of the innocent. These opinions belie a more complex reality, that finance is integral to society, complex financial products have been with us for at least 900 years, that when people, like Aquinas, employ reason and morality to examine the markets there are some surprising conclusions, and that the study of markets leads to profound insights for science in general. Criticism of finance is as likely to reflect a lack of rationality and morality in society, in general, than a specific lack of ethics and reason, in the markets.

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About Me

I am a Lecturer in Financial Mathematics at Heriot-Watt University in Edinburgh. Heriot-Watt was the first UK university to offer degrees in Actuarial Science and Financial Mathematics and is a leading UK research centre in the fields.

Between 2006-2011 I was the UK Research Council's Academic Fellow in Financial Mathematics and was involved in informing policy makers of mathematical aspects of the Credit Crisis.